The One-Dimensional Case

DOI10.1007/978-3-540-89199-4_2zbMath1189.37070OpenAlexW1641171289MaRDI QIDQ3654727

Panayotis G. Kevrekidis

Publication date: 11 January 2010

Published in: Springer Tracts in Modern Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-540-89199-4_2

zbMATH Keywords

Schrödinger equationsolitondiscretesingle dimension

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) NLS equations (nonlinear Schrödinger equations) (35Q55) Special ordinary differential equations (Mathieu, Hill, Bessel, etc.) (34B30) Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems (37K40)

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Onsite and offsite bound states of the discrete nonlinear Schrödinger equation and the Peierls–Nabarro barrier

Cites Work

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• Quantitative measurement of variational approximations
• Asymptotic calculation of discrete non-linear wave interactions
• Stability theory of solitary waves in the presence of symmetry. II
• Breathers in nonlinear lattices: existence, linear stability and quantization
• A perturbation theory for soliton systems
• A perturbational approach to the two-soliton systems
• Discrete solitons in nonlinear Schrödinger lattices with a power-law nonlinearity
• Stability theory of solitary waves in the presence of symmetry. I
• Numerical chaos, symplectic integrators, and exponentially small splitting distances
• The nonlinear Schrödinger equation. Self-focusing and wave collapse
• Stability of bright solitary-wave solutions to perturbed nonlinear Schrödinger equations
• Structural stability of non-ground state traveling waves of coupled nonlinear Schrödinger equations
• On classification of intrinsic localized modes for the discrete nonlinear Schrödinger equation
• Being stable and discrete
• Soliton dynamics in the discrete nonlinear Schrödinger equation
• Stability of discrete solitons in nonlinear Schrödinger lattices
• Stability of waves in discrete systems
• Hamiltonian description of the ideal fluid
• Linear stability of perturbed Hamiltonian systems: theory and a case example
• Analysis of the linearization around a critical point of an infinite dimensional hamiltonian system
• Linearized instability for nonlinear schrödinger and klein-gordon equations
• Instability of standing waves for non-linear Schrödinger-type equations
• Existence and stability of quasiperiodic breathers in the discrete nonlinear Schrödinger equation
• Nonlinear differential−difference equations
• Nonlinear differential–difference equations and Fourier analysis
• The Evans Function and Generalized Melnikov Integrals
• Proof of existence of breathers for time-reversible or Hamiltonian networks of weakly coupled oscillators
• The Mechanism of the Polarizational Mode Instability in Birefringent Fiber Optics
• Existence and stability of standing hole solutions to complex Ginzburg-Landau equations
• Inertia law for spectral stability of solitary waves in coupled nonlinear Schrödinger equations
• Hamiltonian Hopf bifurcation with symmetry
• Counting eigenvalues via the Krein signature in infinite-dimensional Hamiltonian systems
• Counting eigenvalues via the Krein signature in infinite-dimensional Hamiltonian systems
• Stability of waves in perturbed Hamiltonian systems